Iteration Help

[devos]

Hello, I have been going crazy trying to figure this one out. Hopefully someone can help.

I am solving a soil mechanics question using a method called Simplified Bishops Method:

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Please note in the formula for Ψ that F = F.S.

The two equations are dependent on each other. I have tried using goal seek and Data Solver but can't seem to get it to work.

Please see excel sheet attached. Thanks in advance!

Bishops.xlsx

[MrShorty]

Where you have F=f(F), my first thought is to use a numerical technique that I have seen called "method of successive approximations" or "simple iteration". A couple of tutorials on using successive approximations: This first one is more readable and less detailed in explanation. It is also focused on solving quadratic equations, but the basic principle should work very well for your case http://www.chem.purdue.edu/gchelp/ho...approximations
This one goes into some detail, and may not be as readable: http://encyclopedia2.thefreedictiona...s%2c+Method+of

The basic idea is to "guess" at a value for FS, plug that into psi, then calculate a new value for FS. With this new value for FS, go back to psi and calculate psi again, and continue iterating until you are convinced the algorithm is diverging or that it has converged onto a solution.

Programming this sort of thing in a spreadsheet is fairly easy. Are you comfortable setting up a circular reference and turning iteration on (Excel options -- formula options dialog)? If so, you can make a circular reference that will perform the calculation fairly quickly and easily, though the circular nature can make it more difficult to debug the spreadsheet. If you are not comfortable with circular references, set up a block of cells to compute FS from your initial guess of FS, then copy that block across as many copies as you need to see the converged result.

Let us know if you need further assistance.

[devos]

Thanks! I manages to do as you suggested. Your help is much appreciated!